We consider shifted equality sets of the form EG(a,g1,g2) = {ω | g1(ω) = ag2(ω)}, where g1 and g2 are nonerasing
morphisms and a is a letter. We are interested in the family
consisting of the languages h(EG(J)), where h is a coding and
(EG(J)) is a shifted equality set. We prove several closure
properties for this family. Moreover, we show that every
recursively enumerable language L ⊆ A* is a projection
of a shifted equality set, that is, L = πA(EG(a,g1,g2)) for some (nonerasing) morphisms g1 and g2 and a
letter a, where πA deletes the letters not in A. Then
we deduce that recursively enumerable star languages coincide with
the projections of equality sets.

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